A heuristic computational model of basic cellular processes and oxygenation during spheroid-dependent biofabrication

Abstract

An emerging approach in biofabrication is the creation of 3D tissue constructs through scaffold-free, cell spheroid-only methods. The basic mechanism in this technology is spheroid fusion, which is driven by the minimization of energy, the same biophysical mechanism that governs spheroid formation. However, other factors such as oxygen and metabolite accessibility within spheroids impact on spheroid properties and their ability to form larger-scale structures. The goal of our work is to develop a simulation platform eventually capable of predicting the conditions that minimize metabolism-related cell loss within spheroids. To describe the behavior and dynamic properties of the cells in response to their neighbors and to transient nutrient concentration fields, we developed a hybrid discrete-continuous heuristic model, combining a cellular Potts-type approach with field equations applied to a randomly populated spheroid cross-section of prescribed cell-type constituency. This model allows for the description of: (i) cellular adhesiveness and motility; (ii) interactions with concentration fields, including diffusivity and oxygen consumption; and (iii) concentration-dependent, stochastic cell dynamics, driven by metabolite-dependent cell death. Our model readily captured the basic steps of spheroid-based biofabrication (as specifically dedicated to scaffold-free bioprinting), including intra-spheroid cell sorting (both in 2D and 3D implementations), spheroid defect closure, and inter-spheroid fusion. Moreover, we found that when hypoxia occurring at the core of the spheroid was set to trigger cell death, this was amplified upon spheroid fusion, but could be mitigated by external oxygen supplementation. In conclusion, optimization and further development of scaffold-free bioprinting techniques could benefit from our computational model which is able to simultaneously account for both cellular dynamics and metabolism in constructs obtained by scaffold-free biofabrication.

Biofabrication strategies for 3D in vitro models and regenerative medicine

“…Bioprinting into a granular medium allows the fabrication of structures from a range of materials and supports scaffold-free deposition of cells 38 , facilitating the direct deposition of cell aggregates 39 . Therefore, the amount of biomaterial required to deposit cells can be reduced to better reflect the architecture of native tissues 40 . For example, cell-sheet-based bioinks 41 enable the bioprinting of cell aggregates to compose dense cellular structures 42 .…”

Unification of aggregate growth models by emergence from cellular and intracellular mechanisms

“…The modelling of diffusive oxygen in is performed by solving a parabolic partial differential equation. For oxygen concentration c = c ( x , t ), homogeneous diffusivity D = 2500 μm 2 [ 20 ] and source field s = s ( x , t ) = −0.5 fmol/cell s −1 [ 20 ], where x i ∈ x is along the i th dimension of , s maps respiration in onto the rate of oxygen and t = βk is the physical time related to simulation step k by the modelling coefficient β = 0.1 s/MCS [ 40 ], which was chosen to be sufficiently large so that chemical diffusion occurred much faster than cellular motility. The system is solved using a second-order central difference scheme of , forward Euler explicit integration of time and a prescribed boundary condition that all medium sites remain at an environmental concentration of 0.2 mM [ 20 , 32 ].…”

“…More generally, individual cellular mechanisms have been simulated to study their effects on emergent behaviour, including mechanisms affecting aggregate interface morphology and the origin of global shape changes during growth [ 36 ], regulation of cell proliferation during growth by cell compressibility and contact inhibition [ 37 ] or cell deformation [ 38 ], and space-limited mitosis and resulting logistic model behaviour during monolayer growth [ 39 ]. Simulations of scenarios in scaffold-free biofabrication have demonstrated the effects of insufficient oxygenation on oversized spheroids and the potential for environmental control during in vitro fabrication of tissue [ 40 ].…”

“…In this work, a hybrid CPM was developed and employed to explain the disagreement among the classical models of diffusion-limited growth in silico as emergent behaviours from the same multiscale model system. This was accomplished by representing the intracellular processes associated with cell proliferation and death as stochastic functions of internal chemical conditions using Gaussian distributions [ 40 ] for a single diffusive nutrient provided by the environment. In this paradigm, parameters of the stochastic functions represent phenotype-specific genetic regulation by which each cell responds to its local oxygen such that a set of model parameter values is an identifier of a specific cell phenotype.…”

Progress in scaffold‐free bioprinting for cardiovascular medicine

“…Nevertheless, as a branch of bioengineering the scaffold-free biofabrication remains a quantitative discipline, with the potential to benefit from advanced analytics and biosensors, molecular-level optimization and computer modelling. [30][31][32]…”